Understanding Composite Fields and Scalar Fields

[Neitrino]

Dear PF,

Can I consider the composite field for instance psi_bar psi as a scalar filed?
I mean can it be the same in all respects? Can this composite field and scalar filed treated as totally equivalent?

Thks

 

[Perturbation]

Well it is a scalar field. \bar{\psi}\psi is the simplest Lorentz scalar one can construct from the Dirac spinor \psi.

 

[Neitrino]

Suppose I have only fermions and due to some reason fermion-antifermion pairs generate condensate condensate, so SU(N)left*SU(N)right symmetry reduced to SU(N)diag symmetry. Here one says that due to Goldstone theorem there should emerge massles Goldstone bosons. But in proof of goldstone theorem the translation invariance is very essential... so if I treat psi_bar psi as a scalar composed from dirak spinors then this scalar has singularity because product of local operators can have singularities. Making point splitting psi(x+epsilon)psi_bar (x-epsilon) we avoid singularty, but lose translational invariance which is very essential in proof of Goldstone theorem, so in fermion field symmetry breaking Goldstone theorem is no defined well? so psi_bar psi is no "good" scalar filed ?

 

[Neitrino]

just another question - can massive particles form massles bound state?